Theory of Dispersion, Growth, and Damping of Kinetic Linear Electrostatic Waves in Quantum Plasma

In this thesis, the properties of kinetic linear electrostatic waves in non-relativistic unmagnetized ideal plasmas subject to quantum dynamical and statistical effects are determined over a wide range of wavelengths and background electron distributions using a well-known response function derived from quantum kinetic theory. The real part of the frequency (dispersion) and imaginary part of the frequency (damping or growth rate) are plotted as functions of the background parameters. Both stable and unstable situations are analyzed in which up to two particle distributions exist. These distributions have independent total number densities and velocity profiles. Distributions considered are a cold delta-function beam, a class of analytically convenient distributions based on the Cauchy profile, and the quantum thermal equilibrium Fermi-Dirac (FD) distribution. Specific cases considered are an unmagnetized single-population Fermi-Dirac distribution, equal-density counter-drifting FD distributions with no magnetic field, FD distribution with a cold delta-function beam. Prior to this work, waves and instabilities in partially or totally degenerate plasmas had not been studied in depth. Consequently, short-wavelength phemomena remained poorly understood. The results obtained in the conception of this dissertation provide a comprehensive examination of these waves and instabilities, and indicate that damping and growth rates in regimes of moderate quantum effects may be highly sensitive to the exact plasma temperature and density. This work has potential applications in the study of nanoplasmonics and dense astrophysical plasmas.